I mainly play guitar but sometimes play piano. Occasionally I aspire to improve my skills by practicing - which for me - usually consists of trying to learn to play a more complex passage in a particular song.
Once I figure out how I want to play the particular passage or riff, I then start practicing by playing the passage repeatedly - while attempting to play it correctly to the best of my ability.
If I choose to devote fifteen minutes to working on a particular passage, I could try to play it as fast as I can each time so that I get more repetitions (say 60 reps in the allotted 15 minutes). The faster I try to play it, the more often I will miss a few notes, but I will get more chances. And if I learn to play it faster than real time, it will be easier to play at a slower tempo when I actually perform the passage live for an audience.
Or I could play it more slowly each time - while concentrating on playing each note exactly right. But then I might only get a fourth of the number of reps in during my 15 minutes of practice. And, learning it at a slower tempo than I will be playing it during a live performance, might make it more difficult to play full speed.
So if my ultimate goal is to be able to perform the passage live with few if any mistakes, what is the best approach for getting to that point in the shortest period of time - assuming a set amount of time per day allotted to practice that particular passage?
Should I play it fast and get in more reps, or slowly to be sure I am playing it exactly right each time, which would mean I am going through it far fewer times? Or should I only practice in real time - the way it will be performed?